Existence of solutions to a phase-field model for the isothermal solidification process of a binary alloy

✍ Scribed by J. Rappaz; J. F. Scheid

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 180 KB
• Volume: 23
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/(sici)1099-1476(200004)23:6<491::aid-mma120>3.0.co;2-4

✦ Synopsis

We investigate the well-posedness of a phase-"eld model for the isothermal solidi"cation of a binary alloy due to Warren}Boettinger [12]. Existence of weak solution as well as regularity and uniqueness results are established under Lipschitz and boundedness assumptions for the non-linearities. A maximum principle holds that guarantees the existence of a solution under physical assumptions on the non-linearities.